Analysis of zz-www.sudokuwiki.org-0129-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=129
level: medium
position: 39..1......2.5..3.5..2....8.......9..3..9...7...4.26...1..3.......9..72.94....... initial
Autosolve
position: 39..1...2..2.59.3.5..2.39.8.2.3...9..3..9.2.7..94.26.321..3...9..39..72.94..2.3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 6,7 => CTR => A2: 1,4,8 * PRF # H3: 6,7 => SOL * PRF # H1: 4,5 => SOL * DIS # I2: 1,4 => CTR => I2: 6 * DIS # A2: 6,7,8 => CTR => A2: 1,4 * DIS # A6: 7,8 => CTR => A6: 1 * DIS # B8: 6,8 => CTR => B8: 5 * PRF # E8: 6,8 => SOL * DIS # F8: 6,8 => CTR => F8: 1,4,5 * DIS # A2: 6,8 => CTR => A2: 1,4,7 * CNT 10 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 6,7 => CTR => A2: 1,4,8 * DIS A2: 1,4,8 # B2: 8 => CTR => B2: 6,7 * DIS A2: 1,4,8 + B2: 6,7 # E3: 6,7 => CTR => E3: 4 * PRF A2: 1,4,8 + B2: 6,7 + E3: 4 => SOL * STA A2: 1,4,8 + B2: 6,7 + E3: 4 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 39..1......2.5..3.5..2....8.......9..3..9...7...4.26...1..3.......9..72.94....... | initial |
| 39..1...2..2.59.3.5..2.39.8.2.3...9..3..9.2.7..94.26.321..3...9..39..72.94..2.3.. | autosolve |
| 398617542472859136561243978725386491634195287189472653217534869853961724946728315 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) B3: 6,7 G1: 4,5 G2: 1,4 E6: 7,8 A8: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C3: 1.. / A2 = 1 => 0 pairs (X) / C3 = 1 => 5 pairs (_) C3,H3: 1.. / C3 = 1 => 5 pairs (_) / H3 = 1 => 0 pairs (X) A6,H6: 1.. / A6 = 1 => 6 pairs (_) / H6 = 1 => 0 pairs (X) F8,I8: 1.. / F8 = 1 => 5 pairs (_) / I8 = 1 => 8 pairs (_) D5,D9: 1.. / D5 = 1 => 5 pairs (_) / D9 = 1 => 8 pairs (_) G2,G4: 1.. / G2 = 1 => 5 pairs (_) / G4 = 1 => 0 pairs (X) F1,E3: 4.. / F1 = 4 => 18 pairs (_) / E3 = 4 => 0 pairs (*) E3,E8: 4.. / E3 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) G1,H1: 5.. / G1 = 5 => 5 pairs (_) / H1 = 5 => 0 pairs (X) B6,H6: 5.. / B6 = 5 => 0 pairs (X) / H6 = 5 => 8 pairs (_) B6,B8: 5.. / B6 = 5 => 0 pairs (X) / B8 = 5 => 8 pairs (_) H1,H3: 7.. / H1 = 7 => 6 pairs (_) / H3 = 7 => 0 pairs (*) C7,C9: 7.. / C7 = 7 => 5 pairs (_) / C9 = 7 => 5 pairs (_) G4,G7: 8.. / G4 = 8 => 8 pairs (_) / G7 = 8 => 5 pairs (_) * DURATION: 0:00:20.538206 START: 05:55:42.696993 END: 05:56:03.235199 2017-05-01 * CP COUNT: (14) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,E6,G1,G2) * 39..1...2..2.59.3.5..2.39.8.2.3...9..3..9.2.7..94.26.321..3...9..39..72.94..2.3.. * PAIR B3: 6,7 BLK 1 A2: 6,7,1,4,8 # reduction candidate for 6,7 A2: 6,7 => CTR * 394.1.5.2.82.59.3.561243978.2.3...95.3..9.2.7..94.26.321..3...9..39..72.94..2.3.. A2: 1,4,8 # 6 pairs B2: 6,7,8 # reduction candidate for 6,7 B2: 6,7 # 10 pairs * PAIR B3: 6,7 ROW 3 E3: 6,7,4 # reduction candidate for 6,7 E3: 6,7 # 18 pairs H3: 6,7,1,4 # reduction candidate for 6,7 H3: 6,7 => SOLVED * 398617542472859136561243978725386491634195287189472653217534869853961724946728315 H3: 1,4 # 12 pairs * PAIR G1: 4,5 BLK 3 H1: 4,5,6,7 # reduction candidate for 4,5 H1: 4,5 => SOLVED * 398617542472859136561243978725386491634195287189472653217534869853961724946728315 H1: 6,7 # 6 pairs * PAIR G1: 4,5 COL G G4: 4,5,1,8 # reduction candidate for 4,5 G4: 4,5 # 6 pairs G7: 4,5,8 # reduction candidate for 4,5 G7: 4,5 # 8 pairs * PAIR G2: 1,4 BLK 3 I2: 1,4,6 # reduction candidate for 1,4 I2: 1,4 => CTR * 394.1.5.2..2.59.3.5.12439.8.2.3...95.3..9.2.7.594.26.321..3...9..39..72.94..2.3.. I2: 6 # 10 pairs H3: 1,4,6,7 # reduction candidate for 1,4 H3: 1,4 # 12 pairs * PAIR G2: 1,4 ROW 2 A2: 1,4,6,7,8 # reduction candidate for 1,4 A2: 6,7,8 => CTR * 394.1.5.2..2.59.3.5.12439.8.2.3...95.3..9.2.7.594.26.321..3...9..39..72.94..2.3.. A2: 1,4 # 10 pairs * PAIR G2: 1,4 COL G G4: 1,4,5,8 # reduction candidate for 1,4 G4: 5,8 # 6 pairs G4: 1,4 # 5 pairs * PAIR E6: 7,8 BLK 5 E4: 7,8,6 # reduction candidate for 7,8 E4: 7,8 # 8 pairs F4: 7,8,1,5,6 # reduction candidate for 7,8 F4: 7,8 # 11 pairs * PAIR E6: 7,8 ROW 6 A6: 7,8,1 # reduction candidate for 7,8 A6: 7,8 => CTR * 398614572472859136561273948.2.3.5894.34.9.257.5948261321..3.4.9..394172594..2.3.1 A6: 1 # 6 pairs B6: 7,8,5 # reduction candidate for 7,8 B6: 7,8 # 8 pairs * PAIR A8: 6,8 BLK 7 C7: 6,8,5,7 # reduction candidate for 6,8 C7: 6,8 # 12 pairs B8: 6,8,5 # reduction candidate for 6,8 B8: 6,8 => CTR * 39681457218275943657.2639.862.375.94.3.19625775948261321..3...986394172594..2.3.1 B8: 5 # 8 pairs C9: 6,8,5,7 # reduction candidate for 6,8 C9: 6,8 # 9 pairs * PAIR A8: 6,8 ROW 8 E8: 6,8,4 # reduction candidate for 6,8 E8: 6,8 => SOLVED * 398617542472859136561243978725386491634195287189472653217534869853961724946728315 E8: 4 # 18 pairs F8: 6,8,1,4,5 # reduction candidate for 6,8 F8: 6,8 => CTR * 39..145.2..2.59.3656.2739.8.2.367.94.3..9.2.717948265321..3...9.5394.72194..2.3.5 F8: 1,4,5 # 5 pairs * PAIR A8: 6,8 COL A A2: 6,8,1,4,7 # reduction candidate for 6,8 A2: 6,8 => CTR * 394.1.5.2..2.59.3.5.12439.8.2.3...95.3..9.2.7.594.26.321..3...9..39..72.94..2.3.. A2: 1,4,7 # 5 pairs A4: 6,8,1,4,7 # reduction candidate for 6,8 A4: 6,8 # 11 pairs A5: 6,8,1,4 # reduction candidate for 6,8 A5: 6,8 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0129-base-pr-000.dot * REASONING * DIS # A2: 6,7 => CTR => A2: 1,4,8 * PRF # H3: 6,7 => SOL * PRF # H1: 4,5 => SOL * DIS # I2: 1,4 => CTR => I2: 6 * DIS # A2: 6,7,8 => CTR => A2: 1,4 * DIS # A6: 7,8 => CTR => A6: 1 * DIS # B8: 6,8 => CTR => B8: 5 * PRF # E8: 6,8 => SOL * DIS # F8: 6,8 => CTR => F8: 1,4,5 * DIS # A2: 6,8 => CTR => A2: 1,4,7 * CNT 10 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,E6,G1,G2) * 39..1...2..2.59.3.5..2.39.8.2.3...9..3..9.2.7..94.26.321..3...9..39..72.94..2.3.. * PAIR B3: 6,7 BLK 1 A2: 6,7,1,4,8 # reduction candidate for 6,7 A2: 6,7 => CTR * 394.1.5.2.82.59.3.561243978.2.3...95.3..9.2.7..94.26.321..3...9..39..72.94..2.3.. B2: 6,7,8 # reduction candidate for 6,7 B2: 6,7 # 10 pairs * RESTART * PAIR B3: 6,7 BLK 1 B2: 6,7,8 # reduction candidate for 6,7 B2: 8 => CTR * 39681457218275943657.2639.862.375.94.3.19625775948261321..3...986394172594..2.3.1 * PAIR B3: 6,7 ROW 3 E3: 6,7,4 # reduction candidate for 6,7 E3: 6,7 => CTR * 398614572.72859136561273948125367.94.3..9.2.77.948261321..3...9.8394.72.94..2.3.. E3: 4 => SOLVED * 398617542472859136561243978725386491634195287189472653217534869853961724946728315 * DURATION: 0:00:05.271339 START: 05:56:30.893138 END: 05:56:36.164477 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0129-base-pr-001.dot * REASONING * DIS # A2: 6,7 => CTR => A2: 1,4,8 * DIS A2: 1,4,8 # B2: 8 => CTR => B2: 6,7 * DIS A2: 1,4,8 + B2: 6,7 # E3: 6,7 => CTR => E3: 4 * PRF A2: 1,4,8 + B2: 6,7 + E3: 4 => SOL * STA A2: 1,4,8 + B2: 6,7 + E3: 4 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=129
Solution
position: 398617542472859136561243978725386491634195287189472653217534869853961724946728315 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # A2: 6,7 => CTR => A2: 1,4,8 * INC # A2: 1,4,8 => UNS * INC # B2: 6,7 => UNS * INC # E3: 6,7 => UNS * PRF # H3: 6,7 => SOL * INC # H3: 1,4 => UNS * PRF # H1: 4,5 => SOL * INC # H1: 6,7 => UNS * INC # G4: 4,5 => UNS * INC # G7: 4,5 => UNS * DIS # I2: 1,4 => CTR => I2: 6 * INC # I2: 6 => UNS * INC # H3: 1,4 => UNS * INC # A2: 1,4 => UNS * DIS # A2: 6,7,8 => CTR => A2: 1,4 * INC # G4: 1,4 => UNS * INC # G4: 5,8 => UNS * INC # E4: 7,8 => UNS * INC # F4: 7,8 => UNS * DIS # A6: 7,8 => CTR => A6: 1 * INC # A6: 1 => UNS * INC # B6: 7,8 => UNS * INC # C7: 6,8 => UNS * DIS # B8: 6,8 => CTR => B8: 5 * INC # B8: 5 => UNS * INC # C9: 6,8 => UNS * PRF # E8: 6,8 => SOL * INC # E8: 4 => UNS * DIS # F8: 6,8 => CTR => F8: 1,4,5 * INC # F8: 1,4,5 => UNS * DIS # A2: 6,8 => CTR => A2: 1,4,7 * INC # A2: 1,4,7 => UNS * INC # A4: 6,8 => UNS * INC # A5: 6,8 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 6,7 => CTR => A2: 1,4,8 * INC A2: 1,4,8 # B2: 6,7 => UNS * INC A2: 1,4,8 # B2: 6,7 => UNS * DIS A2: 1,4,8 # B2: 8 => CTR => B2: 6,7 * DIS A2: 1,4,8 + B2: 6,7 # E3: 6,7 => CTR => E3: 4 * PRF A2: 1,4,8 + B2: 6,7 + E3: 4 => SOL * STA A2: 1,4,8 + B2: 6,7 + E3: 4 * CNT 6 HDP CHAINS / 5 HYP OPENED